At the candy shop you see some tasty-looking gumdrops, jellybeans, and mints, each in yellow, blue, and white.
You buy 10 of each kind (90 candies altogether), take them home, and dump them in a bowl.
After an hour of solitary nibbling, the total of yellow gumdrops, blue gumdrops, yellow jellybeans, and blue jellybeans is down to nine.
The bowl contains only half as many yellow candies as gumdrops, half as many mints as white candies, and half as many blue candies as jellybeans.
How many white mints have you eaten?
Solution to the Problem:
You have eaten one white mint.You know that there are twice as many gumdrops as yellow candies and twice as many jellybeans as blue candies.
This can be expressed as the following equation:
(gumdrops + jellybeans) = 2 x (yellow candies + blue candies)
Since you know that the total number of yellow and blue gumdrops and yellow and blue jellybeans is 9, you can rewrite the equation as follows:
(white gumdrops + white jellybeans + 9) = 2 x (yellow mints + blue mints + 9)
You also know that there are twice as many white candies as mints:
(white gumdrops + white jellybeans + white mints) = 2 x (yellow mints + blue mints + white mints)
Examination of the last two equations shows that they are identical except that "white mints" has replaced"9."
Therefore, nine white mints remain, so you have eaten one.
Note: the solution does not determine the distribution of the other candies.
Here's one possible set of remaining candies:
Mints: 9 white, 1 blue, 1 yellow
Gumdrops: 7 white, 2 blue, 5 yellow
Jellybeans: 6 white, 1 blue, 1 yellow
Click here for Sreeroopa Sankararaman's excellent solution
James Alarie wrote:
Whew! I wrote a Perl program to search all one BILLION (!)
possibilities and found 1504 solutions. In every single one, there
were nine white mints remaining. This means that there was exactly 1
mint eaten for all 1504 solutions. I'll be nice and only quote the
first one that I found:
0 yellow gumdrops 0 blue gumdrops 0 white gumdrops 0 yellow jellybeans 9 blue jellybeans 9 white jellybeans 0 yellow mints 0 blue mints 9 white mints 0 total gumdrops 18 total jellybeans 9 total mints 0 total yellow 9 total blue 18 total white
Correctly solved by:
| 1. Sreeroopa Sankararaman | Singapore, Singapore |
| 2. James Alarie | Flint, Michigan |